WATER WAVES IN TRIANGULAR CANALS.
CALIFORNIA UNIV BERKELEY
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The problem considered is the two and three dimensional modes of motion in a triangular canal whose sides form an angle pi alpha o alpha 12 with the horizontal. Using a linearized theory, the problem becomes a boundary value problem for the triangle with mixed boundary conditions. Greens identity is used to convert the problem into an integral equation. In the two dimensional case, the existence and uniqueness of the solution is proved. The solution is at most logarithmically singular at the intersection of the free surface with the sides. For a point spectrum of values of a certain parameter, bounded solutions are obtained. In the case of 45 degrees, the singular solution is constructed explicitly in the form of an infinite series. For the case of three dimensions, the existence of solutions with at most a logarithmic singularity has been proved and a condition for the boundedness of a solution has been obtained. Author